Comparing and Ordering

Unit: Mastering Place Value - Lesson 3 of 10

Grade: 6
Duration: 60 minutes
Class Size: 30 students
Curriculum Reference: Alberta Mathematics Program of Studies (2023)
Strand: Number (Number and Number Relationships)
Specific Learning Outcomes:

• Number and Number Relationships (6NA1.1): Compare and order rational numbers, including decimal numbers to thousandths, using place value understanding.
• Mathematical Processes (6MP1, 6MP3): Develop reasoning skills by using visuals (number lines, place value charts) to describe relationships between numbers.
• Communication and Representation (6MP4): Use appropriate tools and mathematical language to explain reasoning.

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Learning Objectives

By the end of this lesson, students will be able to:

• I can compare and order whole numbers and decimals up to thousandths using place value.
• I can use number lines and place value charts to visually represent and explain comparisons.
• I can explain my reasoning for ordering numbers using mathematical vocabulary.

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Success Criteria

Students will be able to:

• Correctly identify which numbers are greater, less than, or equal by examining digits in different places.
• Place numbers accurately on a number line and a place value chart.
• Use terms like “tenths,” “hundredths,” and “thousandths” confidently when explaining comparisons.
• Demonstrate the ability to sort a set of decimal numbers from least to greatest and vice versa.

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Resources

• Whiteboard and markers
• Pre-printed place value charts (including columns for ones, tenths, hundredths, thousandths)
• Number line strips (0 to 10, marked in tenths)
• Individual whiteboards and markers for students
• Sets of decimal number cards (up to thousandths)
• Projector and interactive place value app (optional, for visual demonstration)
• Dyslexia-friendly worksheets with clear font (e.g., OpenDyslexic) and colour-coded place value sections

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Lesson Procedure

1. Introduction & Activation (10 minutes)

• Begin with a quick review of place value (whole numbers and decimals up to thousandths). Using the whiteboard, write sample numbers like 4.376 and model reading them out loud.
• Ask: “How do digits in different places affect the value of a number?”
• Present the “I can” statements orally and in writing on the board.
• Share examples and non-examples of comparing numbers: 4.376 vs. 4.367. Highlight that digits in the tenths place are compared first, then hundredths, etc.
• Check for understanding with a quick thumb up/down signal after questions.

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2. Guided Practice (15 minutes)

• Whole-Class Number Line Activity: Show a number line (0–10) and place decimal markers at 3.2, 3.25, and 3.205.
• Discuss how to place numbers correctly based on their decimal values.
• Use the place value chart to model why 3.25 is greater than 3.205 by comparing the hundredths and thousandths place digits.
• Invite students to come up and place number cards on the number line and chart, explaining their reasoning aloud.
• Encourage students to use mathematical language such as “tenths,” “hundredths,” “greater than,” and “less than.”

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3. Independent Practice (20 minutes)

• Place Value Chart Sorting: Students receive sets of 10 decimal number cards to order from least to greatest. They place each number on their personal place value charts.
• Number Line Drawing: On individual whiteboards, students draw a small number line and place the numbers accordingly.
• Peer Discussion: Pair students to explain their ordering decisions using the place value vocabulary.
• Teacher circulates to provide support, encouraging precise explanations.

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4. Differentiation Strategies

For Diverse Learners:

• Provide dyslexia-friendly materials: clear fonts, ample spacing, and colour-coded place value columns to support decoding.
• Allow use of calculators to check decimal values.
• Use tactile number cards and place value charts to support multisensory learning.
• Offer sentence frames for peer discussion, e.g., “I compared the ___ place value first because…”

For Advanced Learners:

• Challenge with comparison of larger decimal numbers, including numbers with zeros (e.g., 3.407 vs. 3.470).
• Introduce the concept of negative decimals and compare them on number lines.
• Extension: Create their own sets of decimal numbers and quiz peers on ordering.

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5. Closing and Review (10 minutes)

• Facilitate a brief whole-class discussion, having selected students share their ordering strategies and explanations.
• Use quick formative assessment quiz: present 5 pairs of numbers, students indicate which is greater using thumbs or mini whiteboards.
• Review key vocabulary and reinforce “I can” statements.
• Highlight the importance of place value understanding for comparing decimals.

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6. Assessment & Feedback

• Observation of student participation during guided and independent practice.
• Collection of place value charts and number line whiteboards for informal assessment.
• Anecdotal notes on use of mathematical language and reasoning during peer discussions.

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Home Connection / Extension

• Encourage students to find examples of decimals in a grocery flyer or sports statistics and practice ordering decimals at home.
• Optional challenge: Write a short explanation of how you ordered decimals using place value vocabulary and share with the class the next day.

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Reflection / Teacher Notes

• Note effectiveness of visual supports (number lines, place value charts) in student understanding.
• Adjust pacing for students needing more time with decimal values or place value concepts.
• Monitor engagement during peer explanations to ensure all students practise mathematical communication.
• Reinforce dyslexia-friendly strategies for future lessons.

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End of Lesson 3